Method and device for processing analogue ouput signals from capacity sensors

ABSTRACT

An analogue output signal of a sensor which comprises a carrier signal with a carrier frequency ω C  which is modulated by a measurement size is sampled with a sampling frequency ω A  to receive a sampled sensor output signal. The frequency ω A  of the sampling signal is set so that it is an integer divisor n of the carrier frequency ω C , wherein the phase of the sampling signal is set so that the sampling signal is synchronous to the sensor output signal. The sampled sensor output signal is filtered now to remove periodically repeated signal components from the sampled sensor output signal. Then a filtered useful signal is received, wherein its amplitude is proportional to the measurand detected by the sensor.

[0001] The present invention relates to the reading out of sensors andin particular to the digital processing of senor output signalscomprising a high-frequency carrier signal which is modulated by ameasured value. In the following description of the present inventionreference is made to capacitive sensors for discussing the inventiveconcept, like for example to micro-mechanical rotational rate sensorswhich use the Coriolis power for determining a rotational rate to bedetected.

[0002] Capacitive sensors, like for example micro-mechanical rotationalrate sensors, have a variety of application opportunities. Thus,micro-mechanical rotational rate sensors are for example used in robotsand mounting systems, in medical technology, in cameras for imagestabilizing, in navigation systems, for stabilizing andremote-controlling road and air vehicles and also in airbag andprotection systems. In general, such sensors have a movable mechanicalstructure which is excited to a periodical oscillation. This periodicaloscillation generated by excitement is also referred to as primaryoscillation. If the sensor is subjected to a rotation around an axisperpendicular to the primary oscillation or the primary movement, thenthe movement of the primary oscillation leads to a Coriolis force whichis proportional to the measurand, i.e. the angular velocity. By theCoriolis force a second oscillation orthogonal to the primaryoscillation is excited. This second oscillation which is orthogonal tothe primary oscillation is called secondary oscillation. The secondaryoscillation, which is also referred to as detection oscillation, may forexample be detected by a capacitive measurement method, wherein thecapacitively detected measurand serves as a measure for the rotationalrate operating on the rotational rate sensor.

[0003] In micro-technical sensors, thereby the electronic signalevaluation is of a great importance, as the performance of the overallsensor system is to a large extend determined by the used read out andevaluation electronics. Due to the small dimensions of themicro-mechanical structure of current rotational rate sensors, like forexample the rotational rate sensor DAVED®, which was developed by theInstitute for Micro and Information Technology of theHahn-Schickard-Gesellschaft e.V., very small capacities and capacitychanges, respectively, down to a range of about 10⁻¹⁸ F must bedetected, so that only very small voltages are received as sensor outputsignals which may, however, not be evaluated directly.

[0004] In micro-mechanical rotational rate sensors this sensor outputsignal is mainly limited by the noise of the electronic components ofthe evaluation electronic, as the actual information which is containedwithin the sensor output signal of the rotational rate sensor maygenerally not be differentiated from noise below a certain level and maythen not be detected anymore.

[0005]FIG. 6 shows the block diagram of an exemplary prior capacitivesensor arrangement 300 in the form of a capacitive rotational ratesensor with a connected electronic signal evaluation arrangement 320 todetect and evaluate the capacitively detected measurand, i.e. therotational rate acting on the sensor arrangement 300.

[0006] The capacitive sensor element 300 schematically illustrated inFIG. 6 comprises three input electrode pairs, wherein at the driverinput electrode pair 302, 302′ driver input signals S1, S′1 with thefrequency ω⁺ _(drive), ω⁻ _(drive) are entered, at the electrode pair304, 304′ primary carrier signals S2, S′2 with the frequency ω⁺ _(CP),ω⁻ _(CP) are entered, and at the electrode pair 306, 306′ secondarycarrier signals S3, S′3 with the frequency ω⁺ _(CS), ω⁻ _(CS) areentered. The indices (+/−) thereby indicate a phase-shifting of therespective signals of 180°, so that the signal S1 is phase-shifted by180° to S′1, the signal S2 is phase-shifted by 180° to S′2 and thesignal S3 by 180° to S′3. Due to internal modulation processes withinthe sensor element, the actual sensor output signal at the output 308 ofthe sensor element is an analogue signal, which comprises theinformation about the detected measurand, e.g. about the presentrotational rate, wherein the analogue signal comprises a carrier signalwith a carrier frequency ω_(C), which is modulated by the measurand.

[0007] By the use of high-frequency carrier signals, the signal/noiseratio of the sensor output signal may be improved significantly, whereinin the realization of the signal evaluation electronic with analoguecomponents, the recovery of the useful signal from theamplitude-modulated sensor output signal is performed by a doubledemodulation in the signal evaluation electronic 320.

[0008] The amplitude-modulated sensor output signal is thereby suppliedto an (analog) operation amplifier 322 for an amplification. Theamplified sensor output signal is then supplied to a high-pass filter324 to filter out a constant component, like e.g. a DC-offset of theoperation amplifier and low-frequency proportions, like e.g. ω_(drive),2*ω_(drive), of the analogue sensor output signal. The waveform of theamplified analogue sensor output signal is illustrated as the waveformS4 in FIG. 6. The output signal of the high-pass filter 324 is suppliedto a first demodulator (multiplier I) 326, which realizes a firstdemodulation (multiplication) of the signal S4 using the high-frequencycarrier signal S3. This multiplication is realized by a four-quadrantdifferential amplifier which uses both half-waves of the input signalfor multiplication. As a result a sinusoidal alternating signal S5 isobtained wherein its amplitude is directly proportional to the detectedmeasurand, i.e. to the rotational rate.

[0009] Subsequently, the signal S5 is supplied to a second demodulator(multiplier II) 330 which converts the sinusoidal signal S5 into adirect current signal or a direct current voltage S6, respectively,which is directly proportional to the amplitude of the alternatingcurrent signal and therefore proportional to the measurand. Thismultiplication is performed with a low-frequency DC-voltage which isphase-shifted to the driver voltage S1.

[0010] To explain the above-described known method for reading out andevaluating an analogue sensor output signal in more detail and to beable to compare the same more easily to the inventive read out andevaluation concept later, the principle of the read out and evaluationmethod according to the prior art is illustrated in a summarized wayagain in FIG. 5.

[0011] The carrier signal ω_(C) (e.g. 500 kHz) is fed into thecapacitive sensor 300 in the middle by a signal source 310. The signalsource 310 is an oscillator with a carrier and reference signalgeneration. The output signal of the sensor 300 is read outdifferentially and amplified within the operation amplifier 322. Theamplified output signal is then supplied to the multiplier 326 whichdemodulates the amplified analogue sensor output signal by multiplyingthe same with the reference signal (500 kHz) from the signal source 310.The waveform S5 (see FIG. 6) is then applied to the output of themultiplier 326.

[0012] A major problem referring to this arrangement is, that the firstdemodulation of the sensor signal has to be performed with thehigh-frequency carrier signals (e.g. 500 kHz). In an oversampling of thecarrier signals, a digital signal processor therefore had to work with aclock frequency which is higher than double the carrier frequency, whichmay not be realized reasonably with current digital signal processorsdue to the very extensive calculation operations that would occur.

[0013] A further problem regarding the above-described conventionalsensor arrangement is, that in addition to the inherent noise of thefirst (analog) operation amplifier 322 further noise proportions andamong others temperature drift is introduced into the useful signal bythe electronic evaluation components, whereby the resolution andtherefore the sensitivity and measurement accuracy of the sensorarrangement is affected significantly. This therefore leads to anoperation performance in processing an output signal of a capacitivesensor arrangement which is not optimum.

[0014] Based on the prior art it is the object of the present inventionto provide an improved concept for processing an output signal of asensor in order to improve the measurement accuracy and sensitivity of asensor arrangement.

[0015] This object is achieved by a method for processing an analogueoutput signal of a sensor according to claim 1 and by a device forprocessing an analogue output signal of a sensor according to claim 14.

[0016] The present invention is based on the findings that theprocessing of a sensor output signal of a sensor element, like e.g. acapacitive rotational rate sensor, may be significantly improved by theuse of a digital processing technique.

[0017] According to the present invention, the output signal of a sensorelement is read into a digital signal processor (DSP) with the use of ananalogue to digital converter (A/D converter) using a sample & holdmember, in which the useful signal may then be digitally processed andevaluated.

[0018] In order to suitably render the amplitude-modulated sensor signalprovided with a high-frequency carrier signal for a digital signalprocessor, so that the digital signal processor may determine and outputthe measurand to be detected with a relatively low calculation effort,the principle of the so-called undersampling is used in processing thesensor output signal with the present invention.

[0019] The above-illustrated principle of undersampling according to theinvention may be used for all sensors whose output signal comprises atypical high-frequency carrier signal, which is modulated by ameasurand, e.g. amplitude-modulated, i.e. in particular for capacitivesensors. With this principle, first of all high-frequency carriersignals within the sensor arrangement are modulated upon the measurementsignal and consequently not demodulated with the high-frequency signalas it is known from the prior art, but the measurement signal isconverted into a useful signal which is easy to process for the digitalsignal processor with the use of an A/D converter with a sample & holdmember using a lower sampling frequency.

[0020] With a “suitable” selection of the sampling frequency for theundersampling process, the sampled sensor output signal whose amplitudeis proportional to the measurand may be directly processed digitally bythe digital signal processor in order to determine the measurand.

[0021] In the case of a capacitive rotational rate sensor this meansthat the amplitude of the useful signal is proportional to the capacityof the capacitive sensor element and to the capacity change,respectively, when a differential read-out method is present.

[0022] As it was discussed above, using the present invention theanalogue output signal of a sensor is to be processed advantageously,wherein the analogue sensor output signal comprises a high-frequencycarrier signal which is modulated by a measurand (e.g.amplitude-modulated). The above-mentioned “suitable” selection of thesampling frequency of the sampling signal is of a decisive importance inthe inventive principle of undersampling used.

[0023] In the present invention, the analogue sensor output signal issampled using an A/D converter comprising a sample & hold member,wherein the sampling frequency is set so that the carrier frequency ofthe sensor output signal is an integer multiple of the samplingfrequency.

[0024] As the carrier frequency ω_(C) with capacitive sensors is usuallyhigher than the frequency ω_(drive) of the useful signal by a factor of30-500, the sensor output signal may also be sampled with a lowerfrequency than the carrier frequency in order to be able to reconstructthe useful signal completely, i.e. without information loss. At the sametime, the phase of the sampling signal must be selected so that it issynchronous to the carrier signal in the sensor output signal. This isfor example achieved by a synchronous frequency division of the carriersignal. In order to obtain the useful signal from the sampled sensoroutput signal, the sampled sensor output signal must be filtered, i.e.band-pass filtered, in order to remove periodically repeatedhigher-frequency signal proportions of the sampled signal from the same,wherein the amplitude of the band-pass filtered signal, i.e. the usefulsignal, is proportional to the measurand detected by the sensor. Theband-bass filtering and the further processing and rendering of thesampled sensor is thereby performed digitally in a digital signalprocessor (DSP) downstream to the A/D converter.

[0025] From the received useful signal, the measurand to be detected,like e.g. the rotational rate may be determined from the digital signalprocessor without substantial calculation efforts. As no extensivecalculation operations are required due to the undersampling, thereforethe overall (digital) signal processing and evaluation, i.e. thesampling and filtering of the sensor output signal and the determinationof the measurand may be performed by a digital signal processor.

[0026] Due to the possibility to be able to perform the processing of asensor output signal of a sensor element using a signal processorbasically digitally, a plurality of advantages result.

[0027] The possibility to start the conversion process at an especiallydefined point of time is especially important for the evaluation of thesensor signal in order to guarantee the exact maintenance of theundersampling of the sensor output signal. The corresponding bandwidthof this A/D converter comprising the sample & hold member must thereforebe selected corresponding to the highest signal frequency. A furtheradvantage of this principle is that the conversion from the analogue tothe digital part is performed directly after the first amplification ofthe sensor signal, wherein in this case the useful signal is onlylimited by the inherent noise of the first (analog) amplifier.

[0028] With a capacitive sensor, like e.g. a capacitive accelerationsensor, the useful signal may be directly evaluated using thisundersampling method as the A/D converter maps the spectrum to theoverall frequency area.

[0029] With a suitable selection of the sampling frequency as a directdivisor of the carrier evaluation frequency, the spectrum may be shiftedso that the carriers are shifted into the zero point (f=0 Hz) and theinformation in the amplitude of this signal, i.e. the acceleration(capacity) is directly proportional to the amplitude of the measurementsignal.

[0030] In a differential capacitive read-out method, as it is forexample used in the rotational rate sensor DAVED®, therefore the firstdemodulation stage may be omitted, as this is already performed by thespecial A/D converter. In this case an alternating voltage is obtainedwherein its amplitude corresponds to the rotational rate. If this signalis again demodulated (2. demodulation) then this demodulation iscalculated directly and the corresponding algorithms are directlyperformed in a digital signal processor (DSP).

[0031] The actual information (bit combination proportional to therotational rate) is digitally output from the digital signal processoror may be further processed as a PWM signal (PWM=pulse width modulation)so that with a possible D/A conversion of the useful signal no datalosses and no additional noise, respectively, must be accepted. Withthis method the noise of the electronic circuit may be reduced and theactual resolution capability of the sensor may almost be achieved.

[0032] For the setup of a complete sensor system with differentcapacitive sensors (gyroscope, acceleration sensor, inclination sensoretc.) this read-out method is ideal. In the digital signal processor(DSP) the individual sensor signals may be compared to each other orcalculated, respectively, wherein with optimized regulation algorithmsthe capacity of the overall system may be improved.

[0033] If for example several rotational rate sensors are used togetherin different angle positions, the movement and the velocity of an objectmay be determined. Therefore, low-cost, low-interference (i.e. extremelyreliable) and smallest rotational rate sensors may be realized forspecific tailor-made industrial applications by micro-mechanicalmanufacturing processes. With the inventive digital read out andevaluation method, for example rotation movements up to a range of about0.01° per second may be detected for capacitive rotational rate sensors.

[0034] Due to the reduced signal processing requirements to the digitalsignal processors which are used in the present invention for sensorsignal evaluation, it is possible, that the same take over additionaltasks and functions for each individual sensor or for the overallsystem, like for example an active temperature compensation with thehelp of PI regulators, a self-calibration and a self-diagnosis function.

[0035] In the following, preferred embodiments of the present inventionare explained in more detail with reference to the accompanyingdrawings, in which:

[0036]FIG. 1 shows a block diagram of digital signal evaluationelectronics for a sensor element according to the present invention;

[0037] FIGS. 2A-L show illustrations for explaining the process ofundersampling with the digital evaluation of an output signal of thecapacitive sensor;

[0038]FIG. 3 shows a block diagram of digital signal evaluationelectronics for a capacitive sensor element comprising a primary and asecondary control circuit;

[0039]FIG. 4 shows a principal illustration of the inventive digitalsignal evaluation arrangement;

[0040]FIG. 5 shows a principal illustration of a conventional analoguesignal evaluation arrangement; and

[0041]FIG. 6 shows a block diagram of conventional analogue signalevaluation electronics for a sensor arrangement.

[0042]FIG. 1 shows the block diagram of digital read out and evaluationelectronics 120 for a sensor arrangement 100 according to the presentinvention. The capacitive sensor element 100 corresponds to the sensorelement 300 of FIG. 3 which was already discussed in the descriptionintroduction.

[0043] In the following description of the present invention, forexplaining the inventive concept reference is made to capacitive sensorelements, like e.g. to micro-mechanical rotational rate sensors, whichuse the Coriolis force for determining a rotational rate to be detected.

[0044] The capacitive sensor element 100 schematically illustrated inFIG. 1 comprises three input electrode pairs, wherein at the driverinput electrode pair 102, 102′ driver input signals S1, S′1 with thefrequency ω⁺ _(drive), ω⁻ _(drive) are applied, at the electrode pair104, 104′ primary carrier signals S2, S′2 with the frequency ω⁺ _(CP),ω⁻ _(CP) are arranged, and at the electrode pair 106, 106′ secondarycarrier signals S3, S′2 with the frequency ω⁺ _(cs), ω⁻ _(cs) areapplied. The indices (+/−) thereby indicate a phase-shift of therespective signals by 180°, so that the signal S1 is phase-shifted by180° to S′1, the signal S2 by 180° to S′2 and the signal S3 by 180° toS′3. Due to internal modulation processes within the sensor element theactual sensor output signal at the output 108 of the sensor element isan analogue signal which comprises a high-frequency carrier signal whichis modulated by a measurand. The sensor output signal therefore includesthe information about the detected measurand, e.g. about the presentrotational rate.

[0045] As with capacitive rotational rate sensors very small capacitiesor capacity changes, respectively, down to a range of about 10⁻¹⁸ F mustbe detected, only small voltages are received as sensor output signalswhich may not be evaluated directly. By the use of high-frequencycarrier signals which are modulated with the detected measurand, thesignal/noise ratio of the sensor output signal may be improvedsignificantly.

[0046] As with the sensor arrangement described for the prior art, theamplitude-modulated output signal of the sensor provided with ahigh-frequency carrier signal is first supplied to an (analog) operationamplifier and amplified there.

[0047] The output 108 of the sensor element 100 is interconnected withthe input of digital read out and evaluation electronics 120. At theinput of digital evaluation electronics 120 an operation amplifier 122is arranged, wherein at its input the output signal of the capacitivesensor element 100 is applied. The output of the operation amplifier 102is connected to an analogue high-pass filter 124. The output of thehigh-pass filter 124 is connected to two analog/digital converters 126,128, comprising a sample & hold member. The outputs of theanalog/digital converter 126, 128 are connected to a digital signalprocessor 130.

[0048] The amplified sensor output signal is supplied to the high-passfilter 124, to filter out DC components, like for example a DC offset ofthe operation amplifier and low-frequency proportions of the sensoroutput signal. The waveform of the amplified band-pass filtered sensoroutput signal is illustrated as course S4 in FIG. 1. It may be seen thatthe amplified sensor signal S4 is an amplitude-modulated signal providedwith a high-frequency carrier.

[0049] The digital signal processor 130 provides an output signal at itsoutput which reproduces the measurand detected by the capacitive sensorelement.

[0050] In the following, the functioning of the device and the methodfor processing an analogue output signal (S4) of a sensor (100)according to the present invention is explained.

[0051] In the inventive sensor evaluation arrangement the analoguesensor output signal comprising a carrier signal with a carrierfrequency ω_(C) which is modulated by a measurand is sampled using anA/D converter 126, 128 with a sample & hold member with a samplingfrequency of ω_(A) in order to receive a sampled sensor output signalwhich is present in digital form. The frequency ω_(A) of the samplingsignal is thereby set so that it is an integer divisor n of the carrierfrequency ω_(C), whereby: ω_(C)=nω_(A).

[0052] As it was explained above, by the use of high-frequency carriersignals the signal/noise ratio of the sensor output signal may beimproved significantly, wherein in capacitive sensors the carrierfrequency ω_(C) of the carrier signal is usually set to a frequencyhigher than 250 kHz and which preferably is about 500-750 kHz.

[0053] As the carrier frequency ω_(C) with capacitive sensors is usuallyhigher than the frequency ω_(drive) of the useful signal by a factor of30-500, the sensor output signal may also be sampled with a lowerfrequency than the carrier frequency in order to be able to reconstructthe useful signal completely, i.e. without information loss. At thattime, the phase of the sampling signal must, however, be set so that thesampling signal is synchronous to the carrier signal. This is generallyachieved by a synchronous frequency division of the carrier signal,wherein the carrier frequency ω_(C) of the carrier signal is an integermultiple of the sampling frequency ω_(A), i.e. ω_(C)=nω_(A). The sensoroutput signal is therefore present in digital form as a sequence ofdiscretely sampled values after the sampling by the A/D converter usingthe sample & hold member.

[0054] This sampled sensor output signal which is present in digitalform is further processed digitally in the digital signal processor 130,i.e. among other things it is digitally band-pass filtered, wherein theperiodically repeated higher-frequency signal proportions whosefrequency is higher than ω_(A)/2 are to be removed. Hereby, the cut-offfrequency of the band-pass filter is preferably set to half the samplingfrequency ω_(A)/2 in order to receive the searched useful signal.

[0055] In this connection, reference is made to FIG. 2L for a betterunderstanding, which shows the spectrum of a synchronously undersampledamplitude-modulated signal using band-pass filtering.

[0056] As the amplitude of the currently present useful signal isproportional to the measurand detected by the sensor (100), e.g. therotational rate, the useful signal may be digitally evaluated by asignal processor (130) in order to determine the measurand. The digitalsignal processor (130) will finally output an analogue or a digitalsignal which represents the measurand.

[0057] In summary, it may be seen that the sensor output signal isconverted into a useful signal with the use of the A/D converters 126,128 comprising the sample & hold member using the so-calledundersampling. As a result a sinusoidal signal S5 is present whoseamplitude is directly proportional to the measurand to be measured, i.e.to the rotational rate. This useful signal is read into a digital signalprocessor (DSP) 130 which may further process the useful signal S5without excessive calculation effort in order to determine the measurandand for example output the same as an analogue or a digital signal.

[0058] It is to be noted, that the inventive concept for processing ananalogue output signal of the sensor may be used for all analogue sensoroutput signals, in particular of capacitive sensors, which comprise acarrier signal which is modulated by a measurand.

[0059] In the following, the system-theoretical aspects of the presentinvention on which a realization of the undersampling is based areexplained in more detail.

[0060] Ideal sampling is to represent a continuous signal u(t) by asequence of equidistant impulses at the times t=nT_(A) wherein n=. . .−1, 0, 1, . . . . Thereby, the impulse areas of the respective valuesmust be proportional at the time (nT_(A)) (see FIG. 2A: sample process).

[0061] The sample period T_(A)=1/f_(A) is the distance between thesampling times. For illustrating the sampled functional values pulsesg(t) normalized to 1 are used, as it is illustrated in FIG. 2B (see FIG.2B: dirac and rectangular pulses).

[0062] The description of the sampler is made using a theoretical model.The pulse form of the sampler describes a dirac pulse, the function ε(t)describes a jump function. The sampler may therefore also be describedas a simple model of a multiplier with the input values U_(e1) andU_(e2). The result, the output value u_(a), is again combined with themultiplier constant U_(M): $\begin{matrix}{u_{a} = \frac{u_{e1} \cdot u_{e2}}{U_{M}}} & (1)\end{matrix}$

[0063] With u_(e1)=u(t) and the periodical sequence of dirac pulses$\begin{matrix}{u_{e2} = {u_{\delta} \cdot T_{\delta} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}\quad {\delta \left( {t - {n \cdot T_{A}}} \right)}}}} & (2)\end{matrix}$

[0064] with the voltage-time-area u_(δ)T_(δ) after the insertion, theconversion and the consideration of the relation, it is obtained thatδ(t−nT_(A)) is zero for t≠nT_(A): $\begin{matrix}{u_{a} = {\frac{u_{\delta} \cdot T_{\delta}}{U_{M}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}{{u\left( {n\quad T_{A}} \right)} \cdot \quad {\delta \left( {t - {n \cdot T_{A}}} \right)}}}}} & (3)\end{matrix}$

[0065] Dirac pulses may not be generated in reality, therefore a shapingfilter follows the multiplier in the theoretical model of the sampler,which for example converts the dirac pulse into a rectangular pulse.

[0066] Thus, the model of a sampler illustrated in FIG. 2C is obtained.

[0067] The principal idea of the present invention now is to use thismultiplier as a mixer and as the first demodulation stage.

[0068] In order to be able to explain the principle in more detail,further considerations are, however, required especially in the spectralarea.

[0069] The shaping filter replaces the term δ(t−n·T_(A)). As a formulafor the real sampler the following is obtained: $\begin{matrix}{u_{a} = {\frac{u_{\delta} \cdot T_{\delta}}{U_{M}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}{{u\left( {n\quad T_{A}} \right)} \cdot \frac{{ɛ\left( {t - {n \cdot T_{A}}} \right)} - {ɛ\left( {t - \tau - {n \cdot T_{A}}} \right)}}{\tau}}}}} & (4)\end{matrix}$

[0070] The height u_(A)(nT_(A)) of a pulse at a location t=nT_(A) istherefore: $\begin{matrix}{{u_{a}\left( {n\quad T_{A}} \right)} = {{\frac{u_{\delta} \cdot T_{\delta}}{U_{M} \cdot \tau} \cdot {u\left( {n\quad T_{A}} \right)}} = {K_{A} \cdot {u\left( {n\quad T_{A}} \right)}}}} & (5)\end{matrix}$

[0071] By way of illustration, the function f(t) is converted to aseries of weighted dirac pulses by an ideal sampler (see FIG. 2D: idealsampler).

[0072] For a calculation in the frequency domain the spectrum of thesampling signal must be calculated. This is done by way ofmultiplication of the spectrum of the ideal sampler with the frequencyresponse of the shaping filter. The frequency response is the Fouriertransform of the pulse response function g(t). By the Fouriertransformation of the function $\begin{matrix}{{g(t)} = \frac{{ɛ(t)} - {ɛ\left( {t - {\tau \cdot}} \right)}}{\tau}} & (6)\end{matrix}$

[0073] a complex frequency response $\begin{matrix}{{F_{F}(f)} = {\frac{\sin \left( {\pi \cdot f \cdot \tau} \right)}{\pi \cdot f \cdot \tau} \cdot ^{{- j}\quad {n \cdot f \cdot \tau}}}} & (7)\end{matrix}$

[0074] of the shaping filter is obtained.

[0075] The spectrum of the ideal sampler is obtained by developing thedirac pulse sequence δ_(per)(t) in a Fourier sequence $\begin{matrix}{{\delta_{per}(t)} = {{\sum\limits_{n = {- \infty}}^{+ \infty}{\delta \left( {t - {n \cdot \quad T_{A}}} \right)}} = {\frac{1}{T_{A}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}^{{- j}\quad {2 \cdot \pi \cdot n \cdot f_{A} \cdot t}}}}}} & (8)\end{matrix}$

[0076] and inserting the same into the equation (5) for u_(a)(t). Thenthe following relation is obtained: $\begin{matrix}{u_{a} = {\frac{u_{\delta} \cdot T_{\delta}}{U_{M}T_{A}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}{{u(t)} \cdot ^{j\quad {2 \cdot \pi \cdot n \cdot f_{A} \cdot t}}}}}} & (9)\end{matrix}$

[0077] With the use of the Fourier transformation $\begin{matrix}{{U(f)} = {\int_{- \infty}^{\infty}{{{u(t)} \cdot ^{{- j}\quad {2 \cdot \pi \cdot n \cdot f_{A} \cdot t}}}\quad {t}}}} & (10)\end{matrix}$

[0078] differential equations are converted into algebraic equations.

[0079] After further transformations and simplifications the followingresults: $\begin{matrix}{{u_{a}(f)} = {\frac{u_{\delta} \cdot T_{\delta}}{U_{M}T_{A}} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}\quad {U\left( {f - {nf}_{A}} \right)}}}} & (11)\end{matrix}$

[0080] This result will be illustrated graphically. The sampling usingan ideal sample & hold member causes a periodical repetition of thespectrum of the signal to be sampled with the multiple of the samplingfrequency f_(A). FIG. 2E shows the spectrum of a signal before and afterthe transformation using an ideal sampler (FIG. 2E: ideal samplingprocess in spectral view).

[0081] The use of the sampler as a demodulation stage is explained inmore detail in the time domain using this knowledge in the frequencyarea and using a graphical illustration of the signals.

[0082] To be able to digitize and afterwards reproduce signalsperfectly, further conditions must be fulfilled. In this connection thisis referred to as sampling theorem. It indicates that the analoguesignal must be band-limited, i.e., above the signal cut-off frequency^(f) ^(_(gs)) no spectral components must be located so that theoriginal signal may be reconstructed again completely withoutinformation loss. For the spectrum U(f) of a signal therefore thecondition U(f)=0 for |f|>f_(gs) must be accepted.

[0083] The sampling frequency f_(A) must therefore be double as high asthe signal cut-off frequency:

f _(A)≧2·f _(gs)  (12)

[0084] Both conditions must be fulfilled to prevent a so-calledaliasing, i.e. an overlapping with the periodic repetition of thespectrum of u(t), as this aliasing effect would otherwise prevent aperfect reproduction of the signal.

[0085] In order to correspond to the sampling theorem, the frequency fordigitizing must therefore be at least double as high as the highestfrequency present in the signal.

[0086] If this condition, i.e. the sampling theorem, is applied toinventive evaluation electronics of a sensor, like e.g. of a capacitiverotational rate sensor, this frequency would have to beF_(A)≧2·(f_(CS)+f_(drive)) or F_(A)≧2·(f_(CP)+f_(drive)), respectively.As the signal/noise ratio, i.e. the quotient from the amplitude of thetransmitted signal to the noise amplitude, should be as high aspossible, the carrier frequency should be as high as possible, e.g.several hundred kHz. If the carrier frequency is therefore 500 kHz orhigher, the sampling rate should consequently be higher than 1 MHz.

[0087] The processing in this clock cycle results in large amounts ofdata. I.e., with a cut-off frequency of 100 Hz of the sensor rotationalrate changes are detected at maximum up to a period time of 10 msec. Theinformation to perfectly map the drive frequency (1-10 kHz) is at 10000oscillations per second. With a carrier frequency of for example 500 kHzthe sampling process must be performed according to the sampling theoremwith a frequency of 1 MHz. This represents a factor of 10000 in relationto the bandwidth of 100 Hz. The sampling must therefore be performedwith the factor 100*10000 (=1*10⁶) due to the high carrier frequencycompared to the necessary information.

[0088] As it is shown in FIG. 2C (model of a sampler), the samplerconsists of a multiplier and a shaping filter. It is therefore obviousto use this characteristic to aim at a so-called intermediate mixing ora synchronous sampling or undersampling, respectively, with certaincharacteristics and limiting values.

[0089] With an intermediate mixing the characteristic is used, that thesignal is identical in the ranges 0 to f_(A) and n·f_(A) to(n+1)·×f_(A), respectively, with an ideal sampler, and that noband-limited signal with a DC proportion should be evaluated. It istherefore possible to “shift” the signal band with the necessaryinformation into a range in which the amounts of data may be processedagain. In FIG. 2F a so-called intermediate mixing is illustrated byf_(A)<f_(CS)+f_(drive).

[0090] With a suitable selection of the sampling frequency it ispossible to shift the useful frequency directly into the zero point andtherefore to realize the first demodulation with the sampling member orwith the integrated analog/digital converter, respectively.

[0091] At that time, an oscillation with the frequency ω₀ with the sameperiod length T_(A)=1/ω₀ is sampled. At a starting point here the idealsampler is used, wherein the integration of the real sampler with thecharacteristic additional frequency response sin(x)/x has no influenceon this consideration.

[0092] The formula for the sampled oscillation with the equation (11)and considering $\begin{matrix}{k_{\delta} = {\frac{u_{\delta} \cdot T_{\delta}}{U_{M}T_{A}} = 1}} & (13)\end{matrix}$

[0093] and

e ^(jx)=cos(x)+j sin(x)  (14)

[0094] and after a simplification is: $\begin{matrix}{{u_{a}(t)} = {\hat{u} \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}{{\cos \left( {\omega_{0}t} \right)} \cdot {{\cos \left( {n\quad \omega_{0}t} \right)}.}}}}} & (15)\end{matrix}$

[0095] Equidistant sampling values with frequency proportions visible inthe spectrum are obtained, which are designated with the index variablen. FIG. 2G shows a spectrum of a synchronously sampled cosineoscillation. The synchronous sampling may be illustrated graphically inthe time domain with the following signal images, wherein FIG. 2H showsthe time course of a synchronously sampled cosine oscillation.

[0096] By this process, the sum of “possible signals” seams endless,i.e. the sampling values are fulfilled by any multiples, starting with“zero” of the sampling frequency. If the signal in digital signalprocessing is regarded from the direct voltage proportion to half of thesampling frequency, this corresponds to a frequency shift into the zeropoint of the frequency axis and therefore to a demodulation. Theseparation of the higher-frequency proportions is done theoreticallywith an ideal low-pass whose cut-off frequency corresponds to half ofthe sampling frequency. $\begin{matrix}{{u_{a}(t)} = \begin{Bmatrix}\hat{u} & {for} & {\omega \leq \frac{\omega_{A}}{2}} \\\quad & 0 & {otherwise}\end{Bmatrix}} & (16)\end{matrix}$

[0097] In a circuit construction this is realized by a low-pass which isas steep as possible, e.g. using software, which attenuates undesiredharmonics as strong as possible.

[0098] As it was illustrated in the previous section, the sampler may beused for a determination of the amplitude and the phase of anoscillation, i.e. as a first demodulation stage, when the samplingprocess is synchronous to the carrier.

[0099] As the factor for the frequency distance from the wave to bedetected to the information-loaded oscillation in the range from 30 to500 (i.e. the ratio of the frequency of the carrier signal to thefrequency of the useful signal), not every synchronous value needs to beused, so that a further under-sampling of the signal is possible.

[0100] The undersampling factor v_(uds) describes the ratios of theoscillation frequency ω_(CS) to the sampling frequency ω_(A).$\begin{matrix}{v_{uds} = \frac{\omega_{CS}}{\omega_{A}}} & (17)\end{matrix}$

[0101] At the following example this process is to be described in moredetail, wherein the factor ^(v) ^(_(ds)) is here for example selected tobe four. An amplitude-modulated signal

U 1(t)=[A·cos(ω₁ t)]·cos(ω_(C) t)  (18)

[0102] serves as an input, which is illustrated spectrally, as it isshown in FIG. 2I. FIG. 2I further shows a spectrum of anamplitude-modulated signal.

[0103] The spectrum consists of two superimposed oscillations with thefrequencies ω_(C)±ω₁. This is transformed using an ideal sampler andillustrated both mathematically and as a spectrum (see FIG. 2J).

[0104] At that time, the sampling frequency ω_(A) is a quarter of acarrier frequency ω_(C), wherein the frequency v_(uds) is four. With thesame preconditions as in the synchronous sampling using equation (15),and in addition using the equations (17) and (18), the output signalU1(t) of the converter is obtained: $\begin{matrix}{{{U1}(t)} = {A \cdot {\sum\limits_{n = {- \infty}}^{+ \infty}\left\lbrack {\left( {{\cos \left( {{\omega_{C}t} + {\omega_{1}t}} \right)} + {\cos \left( {{\omega_{C}t} - {\omega_{1}t}} \right)}} \right) \cdot {\cos \left( {\frac{n}{v_{uds}}\omega_{C}t} \right)}} \right\rbrack}}} & (19)\end{matrix}$

[0105]FIG. 2J shows a spectrum of a synchronously undersampledamplitude-modulated signal.

[0106] When regarding the relevant signals in FIG. 2K, i.e. of thedesignated area between 0 and half the sampling frequency ±ω_(A)/2,using the condition $\begin{matrix}{\frac{n}{v_{uds}} = 1} & (20)\end{matrix}$

[0107] the output signal U1 results:

U 1(t)=A−cos(ω₁ t).  (21)

[0108]FIG. 2K shows a spectrum of a synchronously undersampledamplitude-modulated signal from 0 to ±ω_(A)/2.

[0109] The spectrum of this range from −ω_(A)/2 to ω_(A)/2 is repeatedperiodically after ^(nω) ^(_(A)) ^(/2) to ±ω_(A)/2 using n=[−∞. . .−1,0,1 . . . +≈].

[0110] The further calculation area is limited by an ideal low-pass toω_(A)/2, or the occurring harmonics of the sampled sensor output signalare attenuated as good as possible using a real low-pass, respectively.

[0111] If the signal should be output directly after sampling and ifω_(A)/2 and ω₁ are close to each other, then the following low-pass mustbe of a high order, i.e. very steep-sloped, in order to make theoccurring harmonic disappear as far as possible.

[0112] As it may be noted from the considerations and calculations, theA/D converter may basically be used as the first demodulation stage. TheA/D converter or the sample & hold member, respectively, must fulfillspecial frame conditions which are explained in more detail in thefollowing.

[0113] The most important link between sensor and electronics is the A/Dconverter with its special characteristics. The digital processing ofthe sensor signal requires the direct transfer into a sequence ofnumbers by sampling without information loss. The so-called sample &hold member is to work almost as an ideal sampling member in thisapplication, i.e. this member may only withdraw very short “samples” ofthe sensor signal. In this case, so to speak pinprick-like taps of thesignal must be performed and therefore the acquisition time, i.e. thetime in which the samples are taken, is of a major importance.

[0114] With the inventive electronic evaluation arrangement for adigital evaluation of the output signals of capacitive sensor elementsmany advantages over conventional analogue evaluation electronics areachieved.

[0115] For a better understanding and for clarifying the advantageoustechnical concept of the present invention now the principles of theinventive read-out method are directly compared to the known read-outmethod illustrated in FIG. 5 using FIG. 4.

[0116] As it was already performed with regard to FIG. 5, the amplifiedanalogue sensor output signal is demodulated in the read-out methodaccording to the prior art, by multiplying the signal with the carrierfrequency (e.g. 500 kHz) (see FIG. 5).

[0117] In the inventive concept for digitally reading out a capacitivesensor, as it is basically illustrated in FIG. 4, the carrierfrequencies in the middle of the sensor 100 are fed in from a signalsource 110, i.e. the carrier and driver signals are internally fed in ata common center electrode of the capacitive sensor 100, wherein thesensor output signal is tapped on the exterior at the exteriorelectrodes of the capacitive sensor 100. The sensor signal isdifferentially read out and amplified using the operation amplifier 122.The amplified analogue sensor output signal is now demodulated using ananalog/digital converter having a sample & hold member, wherein thesampling signal provided by the signal source 110 is an integer divisorof the carrier frequency. This is usually achieved by a synchronousfrequency division of the carrier signal in the signal generator, sothat the sampling signal is synchronous to the carrier signal. At theoutput of the analog/digital converter 126 now the signal course S5 (seeFIG. 1) is present in digital form as the sequence of discretely sampledvalues. This digital signal may now be processed further with arelatively low calculation effort by the digital signal processor 130.

[0118] It is, however, equally possible using the inventive evaluationarrangement that the carrier and driver signal are fed in at theexterior of the exterior electrodes 102-106, 102′-106′ of the capacitivesensor, wherein the sensor output signal may then be tapped at thecommon center electrode 108 of the sensor 100, as it is for exampleshown in FIG. 1.

[0119] By the comparison of the inventive read-out method illustrated inFIG. 1 and the read-out method according to the prior art illustrated inFIG. 5 it is made clear that with the so-called undersampling technique,due to the basically complete digital processing of the sensor outputsignal, which is further possible with a relatively low calculationeffort for the digital signal processor, a plurality of advantages maybe achieved.

[0120] The possibility to start the conversion process at an especiallydefined point of time is especially important for the evaluation of thesensor signal in order to guarantee the exact maintenance of theundersampling of the sensor output signal. The corresponding bandwidthof this A/D converter comprising the sample & hold member must thereforebe selected corresponding to the highest signal frequency. A furtheradvantage of the principle is, that the conversion from the analogue tothe digital part is performed directly after the first amplification ofthe sensor signal, wherein in this case the useful signal is onlylimited by the inherent noise of the first (analog) amplifier. At thattime it is to be noted that the quantizing noise of the A/D converter isdrowned out by the noise of the sensor.

[0121] In a capacitive acceleration sensor the useful signal maytherefore be directly evaluated with the use of this under-samplingmethod, as the A/D converter maps the spectrum to the overall frequencyarea. With a suitable selection of the sampling frequency as a directdivisor of the carrier evaluation frequency, the spectrum may be shiftedso that the carriers appear as a DC voltage and the information in theamplitude of this signal, i.e. the acceleration (capacity), is directlyproportional to the amplitude of the measurement signal.

[0122] With a capacitive read-out method, at it is for example used withthe rotational rate sensor DAVED®, the first demodulation stage may beomitted, as this is already performed by the special A/D converter. Inthis case an alternating signal is received whose amplitude correspondsto the measured rotational rate. If this signal is demodulated again(second demodulation) then this demodulation is digitally calculated andthe corresponding algorithms are directly performed in a digital signalprocessor (DSP).

[0123] The actual information (bit combination proportional to therotational rate) is digitally output from the digital signal processoror may be further processed as the PWM signal (PWM=pulse widthmodulation), in order to not to have to accept data losses or anadditional noise, respectively, in a possible D/A conversion of theuseful signal. With this method the noise of the electronic circuit maybe reduced and the actual resolution capability of the sensor may almostbe achieved.

[0124] For the construction of a complete sensor system with differentcapacitive sensors (gyroscope, acceleration sensor, inclination sensor,etc.) this read-out method is ideal. In the digital signal processor(DSP) the individual sensor signals may be compared to each other andcalculated, respectively, wherein with optimized regulation algorithmsthe performance capacity of the overall system may be improved.

[0125] If, for example, several rotational rate sensors in differentangle positions are used together, the movement and the velocity of anobject may be determined. By micro-mechanical manufacturing methodstherefore low-cost, low-interference (i.e. extremely reliable) andsmallest rotational rate sensors for specific tailor-made industrialapplications may be realized. With the inventive digital read-out andevaluation method rotary movements down to a range of about 0.01° persecond may be detected for capacitive rotational rate sensors.

[0126] Due to the decreased requirements and capacity utilization of thedigital signal processors which are used for the sensor signalevaluation in the present invention, it is possible, that these maketake over additional tasks and functions for each individual sensor orfor the overall system due to the velocity and flexibility, like forexample an active temperature compensation using PI regulators, aself-calibration and a self-diagnosis function.

[0127] Referring to FIG. 3 now the practical construction of aninventive digital sensor signal read-out arrangement in the form of ablock diagram of digital evaluation electronics for a capacitive sensorelement comprising primary and secondary control circuits is discussed.It is to be noted that the elements in FIG. 3 which correspond to thecorresponding elements of FIG. 1 are provided with the same referencenumerals.

[0128] The sensor used herein corresponds to the capacitive sensor 100of FIG. 1, wherein the input 102 is provided for the driver signal S1(ω⁺ _(drive)), the input 102′ is provided for the driver signal S′1 (ω⁻_(drive)) phase-shifted by 180°, the input 104 is provided for thecarrier signal S2 (ω⁺ _(CP)), the input 104′ is provided for the carriersignal S′2 (ω⁻ _(CS)) phase-shifted by 180°, the input 106 is providedfor the carrier signal S3 (ω⁺ _(CS)) and the input 106′ is provided forthe carrier signal S′3 (ω⁻ _(CS)) phase-shifted by 180°. The inputs 104,104′, 106, 106′ for the primary and secondary carrier signals S2 (ω⁺_(CP)), S′2 (ω⁻ _(CS)), S3 (ω^(+CS)), S′3 (ω⁻ _(CS)) are fed by thesignal generator 110, wherein the inputs 102, 102′ of the sensor 100 arefed by an amplifier 111 using an amplification factor of +1 or −1,respectively. The output signal of the sensor 100 is amplified by theanalogue amplifier 122. The amplified analogue sensor output signal isfiltered by the analogue high-pass filter 124.

[0129] The output signal of the filter 124 is now fed to bothanalog/digital converters 126, 128 which sample the amplified filteredanalogue sensor output signal using the so-called undersamplingtechnology using a frequency which is on the one hand synchronous to thefrequency of the carrier signal and on the other hand an integer divisorof the frequency of the carrier signal. The sampling frequency isthereby fed into the analog/digital converter 126, 128 by the signalgenerator 110.

[0130] The sensor output signal which is present in a digital form as aconsequence of discretely sampled values after sampling by theanalog/digital converter using the sample & hold member, is now fed intothe digital signal processor 130 which processes the signal from theanalog/digital converter 126 in a primary loop and the signal from theanalog/digital converter 128 in a secondary loop. The digital signalprocessor comprises the digital band-pass filters 132, 134, thedemodulators 136, 138, 140, 142, the digital low-pass filters 144, 146,148, 150, a comparator 152, digital PI regulators 154, 156, 158, 160, aclock 162, a primary sine wave oscillator 164 and a secondary sine waveoscillator 166 as components which are software-implemented, which arearranged and interconnected as illustrated in FIG. 3. The sine waveoscillator 164 is connected to a digital/analogue converter 168 on theoutput side which is again connected to the amplifier 111. The secondarysine wave oscillator 166 is connected to a digital/analogue converter170 and a digital/analogue converter 172 on its output side which areagain connected to an input 106 and an input 106′, respectively, of thesensor 100. The output of the digital PI regulator 158 is connected toan output interface 174 of the digital signal processor 130, at whichthe output signal, i.e. the rotational rate to be detected, is output indigital or also analogue form.

[0131] By the extended implementation of the digital signal evaluationarrangement with a primary and a secondary control circuit, compared tothe conventional arrangement a clearly improved compensation ofenvironmental influences, like for example a temperature drift, may beprovided, so that an excellent frequency and amplitude stabilization ofthe sensor output signal may be achieved.

1. Method for processing an analogue output signal (S4) of a sensor(100), wherein the analogue sensor output signal (S4) comprises acarrier signal having a carrier frequency ω_(C) and being modulated by ameasurand, wherein the method comprises: sampling (126, 128) of theanalogue sensor output signal (S4) using a sampling frequency ω_(A) toobtain a sampled sensor output signal, wherein the sampling frequencyω_(A) of the sampling signal is set to be an integer divisor n of thecarrier frequency ω_(C), and wherein the phase of the sampling signal isset so that the sampling signal is synchronous to the carrier signalω_(C).
 2. Method according to one of the preceding claims, wherein thesampling signal is obtained by a synchronous frequency division of thecarrier signal, wherein the carrier frequency ω_(C) of the carriersignal is an integer multiple n of the sampling frequency ω_(A), with:ω_(C)=nω_(A).
 3. Method according to one of the preceding claims,wherein the carrier frequency ω_(C) of the carrier signal is set to afrequency which is higher or equal to 250 kHz.
 4. Method according toone of the preceding claims, wherein the carrier frequency ω_(C) of thecarrier signal is higher than the frequency ω_(drive) of the usefulsignal by a factor of 30-500.
 5. Method according to one of thepreceding claims, wherein the analogue sensor output signal (S4) isamplified analogously before the step of sampling.
 6. Method accordingto one of the preceding claims, wherein the amplified analogue sensoroutput signal is high-pass filtered before the step of sampling toessentially remove low-frequency components of the signal (S4). 7.Method according to one of the preceding claims, wherein the analoguesensor output signal (S4) is amplitude-modulated by the measurand. 8.Method according to one of the preceding claims, wherein the measurandis a rotational rate.
 9. Method according to one of the precedingclaims, wherein the sensor (100) is a capacitive sensor.
 10. Methodaccording to claim 9, wherein the capacitive sensor (100) is acapacitive rotational rate sensor.
 11. Method according to one of thepreceding claims, wherein the carrier signals are fed into the sensor(100) at a center electrode of the same, wherein the sensor outputsignal is output to exterior electrodes of the sensor (100).
 12. Methodaccording to one of claims 1 to 10, wherein the carrier signals are fedinto the sensor (100) at exterior electrodes of the same, wherein thesensor output signal is output at a common electrode (108) of thesensor.
 13. Method according to one of the preceding claims, wherein theuseful signal is input into a digital signal processor (130), whereinthe digital signal processor outputs an analogue or a digital signalrepresenting the measurand.
 14. Device for processing an analogue outputsignal (S4) of a sensor (100), wherein the analogue sensor output signal(S4) comprises a carrier signal having a carrier frequency ω_(C) andbeing modulated by a measurand, the device comprising: a sampling device(126, 128) for sampling the analogue sensor output signal (S4) with asampling frequency ω_(A) to obtain a sampled sensor output signal,wherein the sampling frequency ω_(A) of the sampling signal is set to bean integer divisor n of the carrier frequency ω_(C), and wherein thephase of the sampling signal is set so that the sampling signal issynchronous to the carrier signal.
 15. Device according to claim 14,wherein the sampling device (100) is an analogue/digital converterhaving a sample & hold member.